Explanation Given data: Refer to the Example 5.15 in the textbook for the required data to estimate the terminal speed of the skydiver at the given elevation. From the example, the mass of the skydiver ( m ) is 75 kg. Cross-sectional area ( A ) is given in the example as 0.72 m 2 . Air density at the given elevation is 4.3% of the surface density. Formula used: Write the expression for drag force of an object as follows. D = 1 4 ρ A v 2 (1) Here, ρ is the density of the air, which is 1.2 kg m 3 at sea level, A is the cross-sectional area of the object, v is the speed (velocity) of the object. Write the expression for equilibrium equation of force for the y -component as follows. ∑ F y = 0 (2) Here, ∑ F y is the sum of the forces in the y -component. Write the expression for force due to weight as follows. w = m g (3) Here, m is the mass of the object (skydiver), and g is the acceleration due to gravity, which is 9.8 m s 2 . Explanation: Given that, the air density at the given elevation is 4.3% of the surface density. As the air density at the sea level (surface density) is 1.2 kg m 3 , the air density for the given elevation is determined as follows. ρ ele = ( 4.3 % ) ρ Substitute 1.2 kg m 3 for ρ , ρ ele = ( 4.3 % ) ( 1.2 kg m 3 ) = ( 4.3 100 ) ( 1.2 kg m 3 ) = 0.0516 kg m 3 The direction of fall of the skydiver is the vertical. The following are the two forces act the skydiver. 1. Drag force on the skydiver, which acts in the upward direction, and 2. Weight of the skydiver due to the gravity of earth, which acts in the downward direction. For the given system, draw the free-body diagram as shown in Figure 1. From the free-body diagram, the drag force acts in the upward direction and the weight acts in the downward direction. Modify the expression in equation (2) for the forces in the y -component as follows. D + ( − w ) = 0 D − w = 0 (4) Here, D is the drag force on the skydiver, and w is the weight of the skydiver due to gravity of the earth. From equation (3), substitute m g for w in equation (4)

4th Edition

ISBN: 9780134779218

Author: Knight

Publisher: PEARSON

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Chapter 5, Problem 40P

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To estimate: The terminal speed of the skydiver.

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Chapter 5, Problem 38P

Chapter 5, Problem 41P

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